Analysis of waveguide antenna arrays with protruding smooth dielectric elements

The two-dimensional problem of radiation from a waveguide array with protruding smooth dielectric elements of arbitrary shape is considered and two approaches for solving that problem are suggested. The first algorithm is based on applying the method of auxiliary sources for the representation of electromagnetic fields outside and inside protrusions in combination with the method of integral equations for the electric field on the waveguide aperture. The point matching of the field tangential components on the protrusion-to-free-space boundary and on the waveguide aperture is used to reduce the problem to a system of linear algebraic equations for the amplitudes of the auxiliary currents and for the amplitudes of the waveguide aperture electric field. The second method is to analyse this structure by the method of volume-integral equations for polarization currents. Results show that the antenna characteristics significantly dependent on the protrusion shape. Examples of the arrays with flat-topped element patterns resulting from geometry numerical optimization are also presented.<>